Divide using synthetic division $$ ( 11x+19 ) \div ( x-6 ) $$

The synthetic division table is:

$$ \begin{array}{c|rr}6&11&19\\& & \color{black}{66} \\ \hline &\color{blue}{11}&\color{orangered}{85} \end{array} $$

The solution is:

$$ \frac{ 11x+19 }{ x-6 } = \color{blue}{11} ~+~ \frac{ \color{red}{ 85 } }{ x-6 } $$

Step 1 : Write down the coefficients of the dividend into division table. Put the zero from $ x -6 = 0 $ ( $ x = \color{blue}{ 6 } $ ) at the left.

$$ \begin{array}{c|rr}\color{blue}{6}&11&19\\& & \\ \hline && \end{array} $$

Step 1 : Bring down the leading coefficient to the bottom row.

$$ \begin{array}{c|rr}6&\color{orangered}{ 11 }&19\\& & \\ \hline &\color{orangered}{11}& \end{array} $$

Step 2 : Multiply by the number on the left, and carry the result into the next column: $ \color{blue}{ 6 } \cdot \color{blue}{ 11 } = \color{blue}{ 66 } $.

$$ \begin{array}{c|rr}\color{blue}{6}&11&19\\& & \color{blue}{66} \\ \hline &\color{blue}{11}& \end{array} $$

Step 3 : Add down last column: $ \color{orangered}{ 19 } + \color{orangered}{ 66 } = \color{orangered}{ 85 } $

$$ \begin{array}{c|rr}6&11&\color{orangered}{ 19 }\\& & \color{orangered}{66} \\ \hline &\color{blue}{11}&\color{orangered}{85} \end{array} $$

Bottom line represents the quotient $ \color{blue}{ 11 } $ with a remainder of $ \color{red}{ 85 } $.

Synthetic Division Calculator